idea

`N.H.F. Beebe and J. Linderberg, Simplifications in the generation and transformation of two‐electron integrals in molecular calculations, Int. J. Quant. Chem. 12, 683-705 (1977)`

first serious realization (also implemented in CFOUR within the MINT integral package)

`H. Koch, A.S. de Merás, T.B. Pedersen, Reduced scaling in electronic structure calculations using Cholesky decompositions, J. Chem. Phys. 118, 9481-9484 (2003)`

efficient realizations (using a two-step procedure for the Cholesky decomposition; also available in CFOUR)

`S.D. Folkestad, E.F. Kjønstad, H. Koch, An efficient algorithm for Cholesky decomposition of electron repulsion integrals, J. Chem. Phys. 150, 194112 (2019)`

`T. Zhang, X. Liu, E.F.Valeev, X. Li, Toward the Minimal Floating Operation Count Cholesky Decomposition of Electron Repulsion Integrals, J. Phys. Chem. A 125, 4258-4265 (2021)`

realization with coupled-cluster and equation-of-motion coupled-cluster theory

`E. Epifanovsky, D. Zuev, X. Feng, K. Khistayev, Y. Shao, A.I. Krylov, General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and qquation-of-motion methods: Theory and benchmarks, J. Chem. Phys. 139, 134105 (2013)`

implementation in CFOUR with quadratically convergent SCF

`T. Nottoli, J. Gauss, F. Lipparini, A black-box, general purpose quadratic self-consistent field code with and without Cholesky decomposition of the two-electron integrals, Mol. Phys. 119, e1974590 (2021) `

implementation in CFOUR with CASSCF

`T. Nottoli, J. Gauss, F. Lipparini, Second-order CASSCF algorithm with the Cholesky decomposition of the two-electron integrals, J. Chem. Theor. Comp. 17, 6819-6831 (2021) `

implementation in CFOUR with CCSD

`T. Nottoli, J. Gauss, F. Lipparini, A Novel Coupled-Cluster Singles and Doubles Implementation that Combines the Exploitation of Point- Group Symmetry and Cholesky Decomposition of the Two-Electron Integrals, J. Chem. Phys. 159, 231101 (2023) `

implementation in CFOUR for relativistic two-component coupled-cluster methods

`C. Zhang, F. Lipparini, S. Stopkowicz, J. Gauss, L. Cheng, Cholesky Decomposition-Based Implementation of Relativistic Two-Component Coupled-Cluster Methods for Medium-Sized Molecules, J. Chem. Theor. Comp. 20, 787-798 (2023) `

implementation in CFOUR for finite-magnetic-field calculations using GIAOs

`S. Blaschke, S. Stopkowicz, Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields, J. Chem. Phys. 156, 044115 (2022) `

`J. Gauss, S. Blaschke, S. Burger, T. Nottoli, F. Lipparini,S. Stopkowicz, Cholesky decomposition of two-electron integrals in quantum-chemical calculations with perturbative or finite magnetic fields using gauge-including atomic orbitals, Mol. Phys. 121, e2101562 (2023) `

geometrical gradients with Cholesky decomposition

`X. Feng, E. Epifanovsky, J. Gauss, A.I. Krylov, Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks, J. Chem. Phys. 151, 014110 (2019)`

geometrical gradients with Cholesky decomposition (non CFOUR implementation)

`A.K. Schnack-Petersen, H. Koch, S. Coriani, E.F. Kjønstad, Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals, J. Chem. Phys. 156, 244111 (2022)`

NMR chemical shifts with Cholesky decomposition (CD-GIAO-MP2)

`S. Burger, F. Lipparini, J. Gauss, S. Stopkowicz, NMR chemical shift computations at second-order Møller–Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals, J. Chem. Phys. 155, 074105 (2021)`

NMR chemical shifts with Cholesky decomposition (CD-GIAO-CASSCF)

`T. Nottoli, S. Burger, S. Stopkowicz, J. Gauss, F. Lipparini, Computation of NMR shieldings at the CASSCF level using gauge-including atomic orbitals and Cholesky decomposition, J. Chem. Phys. 157, 084122 (2022)`